Inflation is an early accelerating phase of the Universe that explains its large-scale smoothness and sows the seeds for the future growth of galaxies and other large-scale structures. Natural Inflation, a model I proposed in 1990 (together with Frieman and Olinto), postulates a new symmetry of nature that ensures the desired properties of inflation, without any unnatural fine-tunings: shift symmetries can naturally provide the required flat potentials. Natural Inflation remains among the most principled theories of the inflaton field, and is a benchmark model for nearly every observational collaboration, including large NASA and ESA missions such as the WMAP and Planck satellites. The original paper has been cited nearly 1000 times, and forms the basis for many of the most recent particle physics models of the inflaton field. I have also proposed another model known as Chain Inflation, in which the Universe tunnels through a series of vacua of ever lower energy. The resulting bubble collisions produce gravitational waves that may have been observed in NANOGRAV data. I continue to work on inflation models and their tests in cosmological data.